The Frank copula

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The Frank copula is a copula that is sometimes used in the modelling of codependency. It is an Archimedean copula, and exchangeable.


Copula name

Frank copula

Common notation




Or if  we use the limit which the independence copula

Kendall’s rank correlation coefficient (for bivariate case)

where  is the Debye function defined as:

Coefficient of upper tail dependence,

Coefficient of lower tail dependence,

Archimedean generator function,

Or if  we use the limit which is taken as

Other comments

If  we obtain the independence copula. The Frank copula (like the Clayton copula) is a comprehensive copula in that it interpolates between a lower limit of the countermonotonicity copula () and an upper limit of the comonotonicity copula ().


Nematrian web functions


Functions relating to the above distribution may be accessed via the Nematrian web function library by using a DistributionName of “Frank Copula”. For details of other supported probability distributions see here.


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